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Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : High School: Algebra

1, 9, 81, 729, 6561...

Is the sequence above arithmetic, geometric, or neither?

Possible Answers:

Arithmetic

Neither

Geometric

Correct answer:

Geometric

Explanation:

The series is geometric, which means that to get from one value to the next you always multiply by the same value. Here to get from one value to the next, you multiply by 9 each time:

1 x 9 = 9

9 x 9 = 81

81 x 9 = 729

729 x 9 = 6561

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Example Question #72 : High School: Algebra

What type of sequence describes the following set of numbers?

3, 15, 75, 375, 1875

Possible Answers:

Arithmetic Series

Geometric Series

Unknown Series

Correct answer:

Geometric Series

Explanation:

This is a geometric series. The same value, 5, is multiplied by each value to get to the next:

3 x 5 = 15

15 x 5 = 75

75 x 5 = 375

375 x 5 = 1875

When each term in a series is equal to the previous term multiplied by the same factor - in this case 5 - that's a geometric series.

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Example Question #1 : Polynomials And Quadratics

Given and find A-B .

$\\A=x^2+2 \\B=4x^2-1$

Possible Answers:

-3x^2-3

-3x^2+3

3x^2+3

-5x^2+3

3x^2-3

Correct answer:

-3x^2+3

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=x^2+2 \\B=4x^2-1$

A-B= (x^2+2)-(4x^2-1)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$A-B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} --1}$

$\\x^2-4x^2=-3x^2 \\2-(-1)=3$

Therefore, the sum of these polynomials is,

-3x^2+3

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Example Question #2 : Polynomials And Quadratics

Given and find A+B .

$\\A=x^2+2 \\B=4x^2-1$

Possible Answers:

5x^2-1

5x^2+3

5x^2+1

3x^2+1

3x^2-1

Correct answer:

5x^2+1

Explanation:

To find the sum of two polynomials first set up the operation and identify the like terms.

$\\A=x^2+2 \\B=4x^2-1$

A+B= (x^2+2)+(4x^2-1)

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -1}$

$\\x^2+4x^2=5x^2 \\2+(-1)=1$

Therefore, the sum of these polynomials is,

5x^2+1

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Example Question #3 : Polynomials And Quadratics

Given and find B-A .

$\\A=x^2+2 \\B=4x^2-1$

Possible Answers:

-3x^2-3

3x^2-3

5x^2-3

-3x^2+3

3x^2+3

Correct answer:

3x^2-3

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=x^2+2 \\B=4x^2-1$

B-A= (4x^2-1)-(x^2+2)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$B-A={\color{Red} 4x^2}{\color{Blue} -1}{\color{Red} -x^2}{\color{Blue} -2}$

$\\4x^2-x^2=3x^2 \\-1-2=-3$

Therefore, the sum of these polynomials is,

3x^2-3

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Example Question #4 : Polynomials And Quadratics

Given and find A-B .

$\\A=3x^3+x+2 \\B=4x^3-2x-1$

Possible Answers:

x^3+3x+3

-x^3-3x-3

x^3+3x-3

-x^3+3x+3

-x^3-3x+3

Correct answer:

-x^3+3x+3

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=3x^3+x+2 \\B=4x^3-2x-1$

A-B= (3x^3+x+2)-(4x^3-2x-1)

The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

Remember to distribute the negative sign to all terms within the parentheses.

$A-B={\color{Red} 3x^3}{\color{Blue} +x}+2{\color{Red} -4x^3}{\color{Blue} +2x}+1$

$\\3x^3-4x^3=-x^3 \\x+2x=3x \\2+1=3$

Therefore, the sum of these polynomials is,

-x^3+3x+3

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Example Question #5 : Polynomials And Quadratics

Given and find A+B .

$\\A=2x^2+2 \\B=4x^2-2$

Possible Answers:

6x^2+2

6x^2+4

6x^2

-6x^2

6x^2-4

Correct answer:

6x^2

Explanation:

To find the sum of two polynomials first set up the operation and identify the like terms.

$\\A=2x^2+2 \\B=4x^2-2$

A+B= (2x^2+2)+(4x^2-2)

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -2}$

$\\2x^2+4x^2=6x^2 \\2+(-2)=0$

Therefore, the sum of these polynomials is,

6x^2

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Example Question #6 : Polynomials And Quadratics

Given and find A-B .

$\\A=2x^2+2 \\B=4x^2-2$

Possible Answers:

2x^2+4

-2x^2-4

-2x^2+4

2x^2-4

-2x^2+2

Correct answer:

-2x^2+4

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=2x^2+2 \\B=4x^2-2$

A-B= (2x^2+2)-(4x^2-2)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$A-B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} +2}$

$\\2x^2-4x^2=-2x^2 \\2+2=4$

Therefore, the sum of these polynomials is,

-2x^2+4

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Example Question #7 : Polynomials And Quadratics

Given and find B-A .

$\\A=2x^2+2 \\B=4x^2-2$

Possible Answers:

2x^2

2x^2-4

-2x^2-4

2x^2+4

-2x^2+4

Correct answer:

2x^2-4

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=2x^2+2 \\B=4x^2-2$

B-A= (4x^2-2)-(2x^2+2)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$B-A= {\color{Red} 4x^2}-2{\color{Red} -2x^2}-2$

$\\4x^2-2x^2=2x^2 \\-2-2=-4$

Therefore, the sum of these polynomials is,

2x^2-4

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Example Question #8 : Polynomials And Quadratics

Given and find A+B .

$\\A=x^2 \\B=4x^2-1$

Possible Answers:

5x^2-1

-5x^2+1

5x^2+1

5x^2

-5x^2-1

Correct answer:

5x^2-1

Explanation:

To find the sum of two polynomials first set up the operation and identify the like terms.

$\\A=x^2 \\B=4x^2-1$

A+B= (x^2)+(4x^2-1)

The like terms in these polynomials are the squared variable.

$A+B={\color{Red} x^2}{\color{Red} +4x^2}-1$

$\\x^2+4x^2=5x^2 \\0+(-1)=-1$

Therefore, the sum of these polynomials is,

5x^2-1

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Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #71 : High School: Algebra

Example Question #72 : High School: Algebra

Example Question #1 : Polynomials And Quadratics

Example Question #2 : Polynomials And Quadratics

Example Question #3 : Polynomials And Quadratics

Example Question #4 : Polynomials And Quadratics

Example Question #5 : Polynomials And Quadratics

Example Question #6 : Polynomials And Quadratics

Example Question #7 : Polynomials And Quadratics

Example Question #8 : Polynomials And Quadratics

All Common Core: High School - Algebra Resources

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